Assessing Atmospheric Variability using Kernel Principal Component Analysis

Abstract A popular methodology to filter seemingly chaotic atmospheric flow into an ordered set of modes of variability is to identify those patterns of geopotential height that occur often. Historically, understanding of the leading patterns or modes of variability was determined through linear statistical methods. Recently, nonlinear methods, such as kernel principal component analysis (KPCA), have been developed that allow for assessing the degree of nonlinearity inherent in the atmospheric flow. By applying KPCA, new modes of variability may be revealed, or current modes may be refined. This study will apply KPCA to filter the atmospheric flow into dominant patterns of 500 hPa Northern Hemisphere geopotential height patterns. Geopotential heights at 500 hPa were drawn from the monthly NCEP/NCAR reanalysis (NNRP) from 1948- present. This research examines the sensitivity of KPCA derived geopotential height patterns drawn from different kernel functions. The research compares the KPCA results of different kernel functions through cross-validation, assessing physical depictions and the generalization of the KPCA for each kernel. Pattern similarity of the cross- validated analyses is assessed, since the magnitude of the height patterns in high-dimensional Hilbert space will be highly dependent on the selected kernel function. The optimal kernel functions are selected using cross-correlations between the cross-validated sets, providing a baseline for future variability studies.